The present invention relates generally to image processing techniques for fringe pattern analysis and, in particular, to optical measurement techniques that utilize phase-shift analysis of a fringe pattern to extract information contained within the fringe pattern.
There are three basic types of fringe patterns used in optical metrology: carrier patterns, Young""s patterns, and phase-shifted patterns. With the continuing advances in image capturing capabilities and increased processing power available from computers and other digital processing devices, automated processes for interpretation of these different types of fringe patterns are continually being developed and refined.
In carrier pattern processing techniques, carrier fringes are utilized to obtain modulated information fringes. The carrier is demodulated afterward in order to retrieve the desired information. See, for example, P. Plotkowski, Y. Hung, J. Hovansian, G. Gerhart, 1985 (xe2x80x9cImprovement Fringe Carrier Technique for Unambiguous Determination of Holographically Recorded Displacements,xe2x80x9d Opt. Eng., Vol. 24, No. 5, 754-756); T. Yatagai, S. Inaba, H. Nakano, M. Suzuki, 1984 (xe2x80x9cAutomatic Flatness Tester for Very Large Scale Integrated Circuit Wafers,xe2x80x9d Opt. Eng., Vol. 23, No. 4, 401-405); and C. Sciammarella, J. Gilbert, 1976 (xe2x80x9cA Holographic-Moirxc3xa9 Technique to Obtain Separate Patterns for Components of Displacement,xe2x80x9d Exp. Mech., Vol. 16, No. 6., 215-219). In these techniques both the pure carrier pattern and modulated pattern are utilized so that the difference can be calculated. See, also, U.S. Pat. No. 5,671,042, issued Sep. 23, 1997 to C. A. Sciammarella, which discloses a holographic moirxc3xa9 interferometry technique using images taken before and after object deformation for purposes of strain measurement.
Another carrier pattern processing approach is the Fourier Transform Method (FTM). See, for example, M. Takeda, H. Ina, S. Kobayashi, 1982 (xe2x80x9cFourier-Transform Method of Fringe-Pattern Analysis for Computer-Based Topography and Interferometry,xe2x80x9d J. Opt. Soc. Am., Vol. 72, No. 1, 156-160), and M. Takeda, Q. Ru, 1985 (xe2x80x9cComputer-based Sensitive Electron-wave Interferometry,xe2x80x9d Appl. Opt., Vol. 24, No. 18, 3068-3071). This FTM approach can be used with single patterns and involves removing the carrier by shifting the spectrum in the frequency domain. However, this spectrum shift introduces error and requires that the carrier fringes be equally spaced. M. Takeda, K. Mutoh, 1983 (xe2x80x9cFourier Transform Profilometry for the Automatic Measurement of 3-D Object Shapes,xe2x80x9d Appl. Opt., Vol. 22, No. 24, 3977-3982) discloses another FTM approach in which carrier information is pre-saved in a computer and the carrier is then removed in the spatial domain. D. Bone, H. Bachor, R. Sandeman, 1986 (xe2x80x9cFringe-Pattern Analysis Using a 2-D Fourier Transform,xe2x80x9d Appl. Opt., Vol. 25, No. 10, 1653-1660A) discloses a refinement of FTM that involves introducing a nonlinear response function and suggests using pure carrier fringe area for carrier demodulation. Yet another refinement is disclosed in J. Gu, F. Chen, 1995 (xe2x80x9cFast Fourier Transformation, Iteration, and Least-Square-Fit Demodulation Image Processing or Analysis of Single-Carrier Fringe Pattern,xe2x80x9d JOSA. Am. A, Vol. 12, No. 10, 2159-2164). This modified FTM technique uses iteration and a global least squares fit to construct the phase of the carrier.
Processing of Young""s patterns is commonly carried out in speckle metrology to obtain optical measurements of deformed objects, including measurements of slope, displacement, strain, and vibration. In speckleometry, two exposures are recorded on a specklegramxe2x80x94one before and one after the object being measured is deformed. The specklegram is then probed pointwise by a narrow laser beam and the resulting Young""s fringes are displayed in a diffraction field behind the specklegram. Various automated systems and algorithms have been proposed, including one-dimensional integration, one-dimensional autocorrelation, one-dimensional and two-dimensional Fourier transformation, two-dimensional Walsh transformation, and maximum-likelihood techniques. See, for example, D. W. Robinson, 1983 (xe2x80x9cAutomatic Fringe Analysis with a Computer Image Processing System,xe2x80x9d Appl. Opt. 22, 2169-2176); J. M. Huntley, 1986 (xe2x80x9cAn Image Processing System for the Analysis of Speckle Photographs,xe2x80x9d J.Phys.E. 19, 43-48); D. J. Chen and F. P. Chiang, 1990 (xe2x80x9cDigital Processing of Young""s Fringes in Speckle Photography,xe2x80x9d Opt. Eng. 29, 1413-1420); J. M. Huntley, 1989 (xe2x80x9cSpeckle Photography Fringe Analysis by the Walsh Transform,xe2x80x9d Appl. Opt. 25, 382-386); and J. M. Huntley, 1992 (xe2x80x9cMaximum-Likelihood Analysis of Speckle Photography Fringe Patterns,xe2x80x9d Appl. Opt. 31, 4834-4838). A whole-field processing approach to analyzing Young""s patterns has been proposed by J. Gu, F. Chen, 1996 (xe2x80x9cFourier-Transformation, Phase-Iteration, and Least-Square-Fit Image Processing for Young""s Fringe Pattern,xe2x80x9d Appl. Opt. 35, 232-239). In the proposed process, two-dimensional fast-Fourier transform (FFT) filtering of a Young""s pattern is used to produce data for an initial phase calculation, following which phase iteration can be used to improve the phase, if desired or necessary. Finally, a global least-squares regression is carried out to fit the phase to a reference plane.
Synchronous detection has been used in processing of carrier and Young""s patterns. See, for example, K. H. Womack, 1984 (xe2x80x9cInterferometric Phase Measurement Using Spatial Synchronous Detection,xe2x80x9d Optical Engineering, Vol. 23, No. 4, 391-395); S. Toyooka, M. Tominaga, 1984 (xe2x80x9cA Spatial Fringe Scanning for Optical Phase Measurementxe2x80x9d); S. Toyooka, Y. Iwaasa, M. Kawahashi, K. Hosoi, M. Suzuki, 1985 (xe2x80x9cAutomatic Processing of Young""s Fringes in Speckle Photography,xe2x80x9d Opt. Lasers Eng., Vol. 6, 203-212); S. Tang, Y. Hung, 1990 (xe2x80x9cFast Profilometer for the Automatic Measurement of 3-D Object Shapes,xe2x80x9d Appl. Opt., Vol. 29, No. 20, 3012-3018); and M. Kujawinska, 1993 (xe2x80x9cSpatial Phase Methods in Interferogram Analysis,xe2x80x9d IOPP, D. Robinson and G. Reid eds., Chapter 5, 180-185).
Synchronous methods utilize a reference spacing for correlation calculation. Generally, the accuracy of the method is determined by how close the reference spacing and the real fringe spacing are to each other. Synchronous methods typically start with either estimating a reference spacing or assuming that the reference spacing is equal to the carrier fringe spacing. Because of the mismatch between the reference spacing and the actual fringe spacing, the method has limited application. As discussed in J. Gu, Y. Shen, 1997 (xe2x80x9cIteration of Phase Window Correlation and Least Square Fit for Young""s Fringe Pattern Processing,xe2x80x9d Appl. Opt., Vol. 36, No. 4, 793-799), synchronous detection can be combined with a least squares fit. Iterations of these two steps and the phase calculation provide good accuracy for Young""s pattern analysis. However, this iteration method is applicable only to equal-spaced fringe patterns and is not useful in analyzing unequally spaced fringe patterns, such as exist when projection fringe patterns are used in three-dimensional (3-D) surface contour measurement.
For purposes of 3-D surface contour measurement, a number of optical projection fringe pattern techniques have been proposed. For example, moirxc3xa9 techniques can be used to obtain surface contour maps, as disclosed in H. Takasaki, 1970 (xe2x80x9cMoirxc3xa9 Topography,xe2x80x9d Appl. Opt., Vol. 9, 1467-1472); D. M. Meadows, W. O. Johnson, J. B. Allen, 1970 (xe2x80x9cGeneration of Surface Contours by Moirxc3xa9 Patterns,xe2x80x9d Appl. Opt., Vol. 9, 942-947); and J. Hovanesian, Y. Hung, 1971 (xe2x80x9cMoirxc3xa9 Contour-Sum Contour-Difference, and Vibration Analysis of Arbitrary Objects,xe2x80x9d Appl. Opt., Vol. 10, 2734). As is known, a moirxc3xa9 fringe pattern is obtained when a reference grating is superimposed over another grating. Projection moirxc3xa9 techniques often utilize a projection of light through a first grating, with the light then being reflected off the object being measured and then viewed through a second grating. See, for example, U.S. Pat. No. 5,307,152, issued April 26, 1994 to A. Broehnlein et al. As disclosed by this patent, phase-shifting interferometry techniques can be used along with the moirxc3xa9 fringe patterns to obtain surface contour information. See also, U.S. Pat. No. 5,202,749, issued Apr. 13, 1993 to K. Pfister, and U.S. Pat. No. 5,069,548, issued Dec. 3, 1991 to A. Boehnlein.
Apart from these dual-grating projection moirxc3xa9 techniques, phase-shifted fringe pattern processing techniques using only a single grating have been proposed for 3-D surface contour measurement. One such common phase-shift technique utilizes four phase-shifted patterns with 90xc2x0 phase differences. See, for example, J. Bruning, D. Herriott, J. Gallagher, D. Rosenfeld, A. White, D. Brangaccio, 1974 (xe2x80x9cDigital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,xe2x80x9d Appl. Opt., Vol. 13, No. 11, 2693-2703); K. Creath, 1985 (xe2x80x9cPhase-Shifting Interferometry,xe2x80x9d Appl. Opt., Vol. 24, No. 18, 3053-3058); and U.S. Pat. No. 5,450,204, issued Sept. 12, 1995 to Y. Shigeyama et al. The phase-shifting can be accomplished physically (i.e., mechanically or otherwise), as in the Shigeyama et al. and Halioua et al. patents, or can be artificially generated from a single image, as discussed in [J. Gu, F. Chen 1996] noted above.
3-D contour measurement systems have also been proposed that use three 120xc2x0 phase shifts, as disclosed in U.S. Pat. No. 4,641,972, issued Feb. 10, 1987 to M. Halioua et al. A two-image phase-shift technique is also known which uses a fast Fourier transformation (FFT) to remove the DC part. See, for example, T. Kreis, 1986 (xe2x80x9cDigital Holographic Interference-Phase Measurement Using the Fourier-Transform Method,xe2x80x9d J. Opt., Soc. Am. A, Vol. 3, No. 6, 847-855). Alternatively, the phase shift can be accomplished in a space domain instead of in a time sequence using a multi-channel phase-shift method such as is disclosed by M. Kujawinska, L. Salbut, K. Patorski, 1991 (xe2x80x9cThree-Channel Phase Stepped System for Moire Interferometry,xe2x80x9d Appl. Opt., Vol. 30, No. 13, 1633-1635).
Spatial-carrier phase-shifting methods (SCPSM) are single pattern analysis techniques. Examples of SCPSM techniques are discussed in Y. Ichioka, M. Inuiya, 1972 (xe2x80x9cDirect Phase Detecting System,xe2x80x9d Appl. Opt., Vol. 11, No. 7, 1507-1514); D. Shough, 0. Kwon, D. Leary, 1990 (xe2x80x9cHigh-Speed Interferometric Measurement of Aerodynamic Phenomena,xe2x80x9d Proc. SPIE, Vol. 1221, 394-403); and M. Pirga, M. Kujawinska, 1995 (xe2x80x9cTwo Directional Spatial-Carrier Phase-Shifting Method for Analysis of Crossed and Closed Fringe Patterns,xe2x80x9d Opt. Eng., Vol. 34, No. 8, 2459-2466). An advantage of these single pattern techniques is that they are suitable for dynamic phenomena. However, in SCPSM the carrier phases typically need to be linear and much bigger than the information phase; that is, much bigger than the phase difference between the phase from the object and that of the reference plane. The carrier phase gradient often has to be aligned along one of the sensor array directions with precise tilt to establish the condition that the consecutive pixels have a 90xc2x0 phase shift. This makes the optical setup difficult and limits the practical application of this approach.
Accordingly, there exists a need for a phase-shift fringe pattern approach to 3-D surface contour measurement that does not require the carrier fringe pattern to be linear or much bigger than the information phase. Moreover, there exists a need for such a system in which the carrier phase need not be accurately aligned relative to the optical sensor array in any prescribed direction.
In accordance with the present invention, there is provided an image processing method for extracting information from a fringe pattern produced by an optical measurement of an object. The method includes the steps of:
(a) recording an image of the fringe pattern;
(b) determining one or more estimated fringe spacings using fringe lines contained within the image;
(c) generating a plurality of phase-shifted image data sets using the image and the estimated fringe spacing(s);
(d) generating wrapped phase information using the phase-shifted image data sets;
(e) unwrapping the phase information and generating a set of data points representative of the unwrapped phase information;
(f) performing at least one iteration of the following steps (f1) and (f2):
(f1) determining an updated estimated fringe spacing for each of a number of the data points using a curve fitting function; and
(f2) repeating steps (c), (d), and (e) using the updated estimated fringe spacings; and
(g) generating output data representing information contained in the fringe pattern using the unwrapped phase information determined during the final iteration of step (e).
Starting with an estimated reference spacing [step (b)], the estimated spacing converges to the true fringe spacing as a result of one or more repetitions of the phase window correlation [step (c)], phase calculation [step (d)], unwrapping [step (e)], and curve fitting [step(f1)]. Preferably, the updated estimated spacing is determined for each selected data point by applying a local least squares fit to at least some of the data points in the region about the selected data point. If necessary or desired, noise suppression using pattern reconstruction and smoothing can be iteratively carried out to improve the signal to noise ratio. Where the unwrapped phase information is stored in memory as an array of data points, the local least squares fit can be carried out using a regression window that comprises a number of data points within the same row as the selected data point, with the regression window being centered on the selected data point.
The phase of the projected fringe pattern does not have to be linear, nor does it have to be much bigger than the information phase. Furthermore, the projected carrier phase need not be aligned relative to the optical sensor in any prescribed direction. This flexibility makes the invention suitable for a number of different optical measurement techniques including, for example, projection moirxc3xa9, speckle, and holographic techniques. Practical applications of the invention include, for example, 3-D surface contour measurement for such purposes as vehicle crash tests, detecting the shape or orientation of a component, or determining the extent of wear on a cutting insert or other machine tool. Moreover, since only a single measured fringe pattern is required, the invention can be used for static, transient, as well as dynamic measurements.